As he has in the past, Law said repeatedly that he relied on the recommendations of subordinates and scattered church records in deciding whether to return priests to parish work even after receiving sexual abuse allegations against them.
Written transcripts and videotapes of Law's June deposition in lawsuits filed against him and others related to alleged abuse by the Rev. Paul Shanley were made public Tuesday.
Also Tuesday, Law resumed giving a deposition behind closed doors.
Shanley, 71, and once known for his street ministry to gay and troubled youths, is in jail awaiting trial on child rape charges. He was indicted in June on charges he abused boys 6 to 15 years old from 1979 to 1989 while he was a priest at a church in suburban Newton.
The Boston Archdiocese is at the center of a nationwide priest sex-abuse scandal that erupted after it was disclosed that Law knew of accusations against former priest John Geoghan but continued to shuffle him between parishes. The archdiocese has been hit with hundreds of allegations against dozens of priests.
Under questioning from Roderick MacLeish, an attorney for Shanley's alleged victims, Law acknowledged that a complaint was sent to the archdiocese in 1966 alleging that Shanley had sexually abused a boy.
But Law said he did not examine Shanley's personnel file, which contained that allegation and others, before promoting Shanley in 1985 to pastor at St. Jean's parish in Newton.
Law also said he did not recall reading a 1985 letter from a woman who said Shanley gave a talk in which he said, "When adults have sex with children, the children seduced them."
MacLeish presented Law with a copy of a letter in which Bishop John McCormack told the woman Law had received her letter.
Law said the church's records were kept in "a lot of disparate places" and that he had no reason to believe Shanley had been abusing children. He has said he had no knowledge of allegations against Shanley until 1993.
"But certainly there was information about Paul Shanley that was not readily available and it would be helpful to have been," Law said.
Also during the deposition, Law was grilled about his handling of the Rev. Daniel Graham. Graham had admitted to child molestation to church officials, but Law allowed him to return to his church in 1988 with no restrictions on his activities.
"He was allowed to continue, yes, after intervention by a medical source," Law said.
Law said he relied on the recommendations of two subordinates in deciding to return Graham to his parish.
Law said that, in accordance with policy that existed at the time, parishioners were not informed of the allegation against Graham.
Law said the policy has changed so that "no priest against whom a credible allegation of sexual abuse against a minor has been made may hold any assignment whatsoever." Such allegations also are reported to law enforcement and the public, he said.
The archdiocese's sex-abuse policy changed most recently in January. Church officials suspended Graham from his ministry in June.
Graham has an unlisted phone number and couldn't be reached for comment. Shanley has pleaded innocent